Journal of Intelligent & Fuzzy Systems - Volume 28, issue 2

Authors: Khan, Madad | Jun, Young Bae | Gulistan, Muhammad | Yaqoob, Naveed

Article Type: Research Article

Abstract: In this paper, we define the concept of generalized cubic subsemigroups (ideals) of a semigroup and investigate some of its related properties. In particular, we introduce the concept of $(\in _{(\widetilde{\gamma }_{1},\gamma _{2}) },\in _{(\widetilde{\gamma}_{1},\gamma _{2}) }\vee q_{(\widetilde{\delta }_{1},\delta _{2})})$ -cubic ideal, $(\in _{( \widetilde{\gamma }_{1},\gamma _{2}) },\in _{(\widetilde{\gamma }_{1},\gamma _{2}) }\vee q_{(\widetilde{\delta }_{1},\delta _{2}) }) $-cubic quasi-ideal, $(\in _{( \widetilde{\gamma }_{1},\gamma _{2}) },\in _{(\widetilde{\gamma }_{1},\gamma _{2}) }\vee q_{( \widetilde{\delta }_{1},\delta _{2})}) $-cubic bi-ideal and $(\in _{( \widetilde{\gamma }_{1},\gamma _{2})},\in _{(\widetilde{\gamma } _{1},\gamma _{2})}\vee q_{(\widetilde{\delta }_{1},\delta _{2})}) $-cubic prime/semiprime ideal of a semigroup.

Keywords: Semigroups, cubic sets, generalized cubic ideals (bi-ideals, interior ideals, quasi ideals, prime ideals)

DOI: 10.3233/IFS-141377

Citation: Journal of Intelligent & Fuzzy Systems, vol. 28, no. 2, pp. 947-960, 2015

Authors: Zheng, Yuhui | Jeon, Byeungwoo | Xu, Danhua | Wu, Q.M. Jonathan | Zhang, Hui

Article Type: Research Article

Abstract: Fuzzy c-means (FCM) has been considered as an effective algorithm for image segmentation. However, it still suffers from two problems: one is insufficient robustness to image noise, and the other is the Euclidean distance in FCM, which is sensitive to outliers. In this paper, we propose two new algorithms, generalized FCM (GFCM) and hierarchical FCM (HFCM), to solve these two problems. Traditional FCM can be considered as a linear combination of membership and distance from the expression of its mathematical formula. GFCM is generated by applying generalized mean on these two items. We impose generalized mean on membership to incorporate …local spatial information and cluster information, and on distance function to incorporate local spatial information and image intensity value. Thus, our GFCM is more robust to image noise with the spatial constraints: the generalized mean. To solve the second problem caused by Euclidean distance (l2 norm), we introduce a more flexibility function which considers the distance function itself as a sub-FCM. Furthermore, the sub-FCM distance function in HFCM is general and flexible enough to deal with non-Euclidean data. Finally, we combine these two algorithms to introduce a new generalized hierarchical FCM (GHFCM). Experimental results demonstrate the improved robustness and effectiveness of the proposed algorithm. Show more

Keywords: Fuzzy C-means, generalized mean, hierarchical distance function, image segmentation, spatial constraint

DOI: 10.3233/IFS-141378

Citation: Journal of Intelligent & Fuzzy Systems, vol. 28, no. 2, pp. 961-973, 2015

Authors: Hu, Xinhua | Zhang, Xumei

Article Type: Research Article

Abstract: With respect to multiple attribute decision making problems with interval intuitionistic trapezoidal fuzzy information, some operational laws of interval intuitionistic trapezoidal fuzzy numbers, score function and accuracy function of interval intuitionistic trapezoidal fuzzy numbers are introduced. An optimization model based on the maximizing deviation method, by which the attribute weights can be determined, is established. For the special situations where the information about attribute weights is completely unknown, we establish another optimization model. By solving this model, we get a simple and exact formula, which can be used to determine the attribute weights. We utilize the interval intuitionistic trapezoidal fuzzy …weighted averaging (IITFWA) operator to aggregate the interval intuitionistic trapezoidal fuzzy information corresponding to each alternative, and then rank the alternatives and select the most desirable one(s) according to the score function and accuracy function. Finally, an illustrative example for evaluating the cluster network competitiveness of small and medium-sized enterprises is given to verify the developed approach and to demonstrate its practicality and effectiveness. Show more

Keywords: Multiple attribute decision making (MADM), maximizing deviation method, interval intuitionistic trapezoidal fuzzy numbers, interval intuitionistic trapezoidal fuzzy weighted averaging (IITFWA) operator, weight information, cluster network competitiveness

DOI: 10.3233/IFS-141381

Citation: Journal of Intelligent & Fuzzy Systems, vol. 28, no. 2, pp. 975-981, 2015

Authors: Hesamian, Gholamreza | Shams, Mehdi

Article Type: Research Article

Abstract: This paper deals with proposing two family of similarity measures between Hesitant Fuzzy Linguistic Term Sets. It will proved that the proposed similar measures satisfy the properties of the axiomatic definition for similarity measures and introduces several theorems. A method is also suggested to rank Hesitant Fuzzy Linguistic Term Sets. Then some desirable properties of the ranking method is put into investigation. An illustrative example from the area of decision making will be used to present the calculation of the similar measures and preference degrees between Hesitant Fuzzy Linguistic Term Sets.

Keywords: Hesitant fuzzy linguistic term set, similarity measure, preference degree, ranking method, reciprocally, reflexivity, transitivity

DOI: 10.3233/IFS-141382

Citation: Journal of Intelligent & Fuzzy Systems, vol. 28, no. 2, pp. 983-990, 2015